NOTE: This applies to all versions before 22.214.171.124. As of now, the prompt to save a password will appear to you using Magic Browser. If you do not wish to go through the below steps, please update your product now by downloading the current version from this link: http://magicdesktop.com/get
Magic Browser uses the preferences and settings of Internet Explorer with regards to extensions, passwords, cookies and automatic filling of forms.
However, by itself, it will not allow you to do these things, as it is meant to be a basic web browsing experience for children.
In order to save passwords or other data in any website for easy and quick navigation, first browse that website through Internet Explorer.
Input all the data it needs and you will be prompted to "remember/save" that password or form data. Once it is saved, exit the website and restart Internet Explorer. Those settings should now be input automatically and you will automatically log on to any website that requires it.
Note however that, if this doesn't happen, Internet Explorer is not allowing you to store personal information. This can be remedied by going into Tools (on the upper right corner of the browser...
... Then choosing Internet Options....
... and ensure the setting "Delete browsing history on exit" is disabled.
Then you can start Magic Browser and websites in which you need to store passwords or form data will load these saved settings on its own.